Meta-heuristic maximum likelihood parameter estimation of the mixture normal distribution for hydro-meteorological variables

Ju Young Shin, Jun Haeng Heo, Changsam Jeong, Taesam Lee

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


In the water resources field, there are emerging problems such as temporal changes of data and new additions of water sources. Non-mixture models are not efficient in analyzing these data because these models are developed under the assumption that data do not change and come from one source. Mixture models could successfully analyze these data because mixture models contain more than one modal. The expectation maximization (EM) algorithm has been widely used to estimate parameters of the mixture normal distribution for describing the statistical characteristics of hydro meteorological data. Unfortunately, the EM algorithm has some disadvantages, such as divergence, derivation of information matrices, local maximization, and poor accuracy. To overcome these disadvantages, this study proposes a new parameter estimation approach for the mixture normal distribution. The developed model estimates parameters of the mixture normal distribution by maximizing the log likelihood function using a meta-heuristic algorithm-genetic algorithm (GA). To verify the performance of the developed model, simulation experiments and practical applications are implemented. From the results of experiments and practical applications, the developed model presents some advantages, such as (1) the proposed model more accurately estimates the parameters even with small sample sizes compared to the EM algorithm; (2) not diverging in all application; and (3) showing smaller root mean squared error and larger log likelihood than those of the EM algorithm. We conclude that the proposed model is a good alternative in estimating the parameters of the mixture normal distribution for kutotic and bimodal hydrometeorological data.

Original languageEnglish
Pages (from-to)347-358
Number of pages12
JournalStochastic Environmental Research and Risk Assessment
Issue number2
Publication statusPublished - 2014 Feb

Bibliographical note

Funding Information:
This research was supported by a grant (11-TI-C06) from Advanced Water Management Research Program funded by Ministry of Land, Infrastructure and Transport of Korean government. The last author also acknowledges that he was supported for this work by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (2012-0362).

All Science Journal Classification (ASJC) codes

  • Environmental Engineering
  • Environmental Chemistry
  • Safety, Risk, Reliability and Quality
  • Water Science and Technology
  • Environmental Science(all)


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